The center of mass is the abbreviation of the center of mass, which refers to an imaginary point in the material system where the mass is considered to be concentrated.AndfocusThe difference is that the center of mass does not have to be in a system with a gravity field.It is worth noting that unless the gravity field is uniform, the center of mass and the center of gravity of the same material system are usually not at the same imaginary point.
The short name of the quality center.The centroid of the particle system is the average position of the mass distribution of the particle system.Let the particle system be composed ofnIt is composed of particles whose masses are
，
，…，
。If used
，
，…，
Respectively indicate that each particle in the particle system is relative to a fixed pointOVector diameter of, using
Represents the vector diameter of the center of mass
Where
centroid
Represents the total mass of the particle system.If different coordinate systems are selected, the specific values of the centroid coordinates will be different, but the relative position of the centroid relative to each particle in the particle system is independent of the selection of the coordinate system.The centroid of the particle system is only related to the relative position of the mass size and distribution of each particle.
Average position of mass distribution of particle system
centroid
Quality CenterIt is independent of the force system acting on the particle system.Let a particle system composed of n particles have masses of m1, m2,..., mn respectively.If r1, r2,..., rn are used to represent the vector diameter of each particle in the particle system relative to a fixed point, and rc is the vector diameter of the center of mass, then rc=(m1r1+m2r2+...+mnrn)/(m1+m2+...+mn).When the object has a continuously distributed mass, the vector radius of the center of mass C rc=ρrdτ/∫ρdτ，WhereρIs the volume (or surface, line) density;dτIs equivalent toρVolume (or surface, line) element of;Integral with distribution densityρOn the whole material body (or surface, line).fromNewton's law of motionOr particle systemMomentum theorem, deductableTheorem of center of mass motion: The motion of the center of mass is the same as that of a particle located at the center of mass. The mass of the particle is equal to the total mass of the particle system, and the force on the particle is equal to the vector sum of all external forces acting on the particle system after translation to this point.It can be inferred from this theorem that:
① The internal force of the particle system cannot affect the motion of the center of mass.
② If the principal vector of the external force on the particle system is always zero, its center of mass isUniform linear motionOr keep still.
③ If the projection of the principal vector of the external force acting on the particle system on an axis is always zero, the coordinate of the center of mass on that axis changes or remains unchanged at a uniform speed.
Any motion of a particle system can generally be decomposed into centroidtranslationAnd relative to the center of mass.The kinetic energy of the particle system relative to a stationary coordinate system is equal to the kinetic energy of the center of mass and the particle system is relative to the center of masstranslationThe sum of the kinetic energy of the motion of the reference frame.The position of the center of mass is of great significance in engineering. For example, to keep the crane stable, the position of the center of mass should meet certain conditions;Aircraft, ship, vehicle, etcMotion stabilityIt is also closely related to the position of the center of mass;In addition, if the center of mass of the high-speed flywheel is not on the rotation axis, it will cause severe vibration and affect the normal work and life of the machine.
That is, when the principal vector of the external force system is equal to zero, the acceleration of the center of mass is equal to zero, and the center of mass remains stationary or keeps constant speed
Linear motion.
(2) If ∑ Fxe ∨ 0, acx=0, vcx=constant
That is, when the algebraic sum of the projection of the external force system on an axis is equal to zero, the acceleration of the center of mass is projected to zero on the axis,
The center of mass keeps still or moves at a constant speed along the axis direction.
These two cases are called the conservation of center of mass motion.The theorem of motion of the center of mass is often used to findRestraint reaction。
Structural model
hydrogen atomElectronic andprotonIt revolves around the center of mass (or centroidal axis) of the hydrogen atom, while electrons and protons are still circling their respective centroidal axesspin----That is, the proof of the atomic centroid structure model.
Centroid of various figures
Abstract: ModernQuantum physicsIs based onrutherfordNucleusFormula structure model (the extranuclear electrons in the atom rotate around the nucleus) andBohrhydrogen atomBased on the hypothesis theory, it mustphysical phenomenonProvide comprehensive, complete, clear, systematic and scientific explanation and proof, such as electronicproton、neutronAnd theirAntiparticleThe spin of, the generation of magnetic moment, decay, annihilation, black hole phenomenon, the problem of antimatter, the nature of electricity, the neutron is unstable when it exists alone, and the atomic nuclear force is very large,gravitational fieldThe production, composition and motion principle of matter are numerous, but they can't. There are too many physical phenomena without scientific explanation and proof, especially forHyperonandExotic particleIt seems that there is another world and supernatural phenomenon. People have been struggling to find the reason. After years of research and calculation, I firmly say that this reason has been found. As long as the nuclear structure model is changed to the atomic centroid structure model (with a proof process),So that a large number of physical phenomena, Bohr's hydrogen atom hypothesis theory and Planck's quantum hypothesis theory, as well as the composition and movement principle of matter can be completely and scientifically explained and proved in theory, and can also be used to explain and prove the Earth, the sun, the solar system anduniverseThe movement, form and composition ofplainGreat changes give the same proof. Theoretically, gold and diamonds can be produced in factories, especially nuclear theory and physicsGrand unified theoryA preliminary explanation will be given.The argument is as follows, and experts, scholars and truth seekers are kindly invited to criticize, correct and learn from it.
Image computing
For a 2D continuous image, f (x, y) ≥ 0. p+q order moment Mpq and central momentμPq is defined as
Where pq is a non negative integer, for the discrete digital image, the above two equations become
Where (ic, jc) is the centroid coordinate, and
It can be seen that the centroid of the image is the 0 th and 1st moment
The second order distance is the radius of rotation
Difference between center of mass and center of gravity
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Center of mass: the center of mass of an object. Center of gravity: the center of gravity of an object.Gravity G=mg, where m is the mass of the object and g is a constant.The center of gravity and the center of mass generally coincide.
reference
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1. Entries Author: Dai Zongxin. Encyclopedia of China, Volume 74 (First Edition) Mechanical Entries: Centroid: Encyclopedia of China Press, 1987:586
